A complete structural model of skeletal muscle by considering the effect of Muscle spindle and Golgi tendon receptors

Subject Areas : Renewable energy

Mahtab Dadkhah ¹ , Mahdi Khezri ² , Hamid Mahmoodian ³

1 - Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 - Digital Processing and Machine Vision Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
3 - Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Received: 2019-11-06 Accepted : 2020-02-29 Published : 2020-05-04

Keywords: Skeletal muscle modeling, Sensory feedbacks, Muscle spindle, Golgi tendon, Muscle tension,

Abstract :

In this study, we try to present a complete model of skeletal muscle, with the aim of expressing it's behavior in a precise manner. This model is presented with considering the role of sensory receptors in muscle function. Muscle spindle and Golgi tendon receptors provide information on length changes and muscle force, respectively . Then this information is sent to the central nervous system for final decision making. In this study, adaptive combination of the Spindle and Golgi tendon afferents Due to the changes in their level of activity and the force produced in the muscle under different functional conditions is suggested. Considering the control feedbacks of the afferents in the presented model can optimize the precise behavior of the muscle under different loads and eliminate the limitations of previous models. The results of the proposed model according to the precise modeling of sensory receptors (Muscle spindle and Golgi tendon) have been consistent with the experimental results of muscle activity. This model can be used to predict muscle's behavior in preventing muscular nervous system damage, as well as the design of artificial muscles and different prostheses.

References:

[1] C. K. Lin, P. E. Crago, "Structural model of the muscle spindle", Annals of Biomedical Engineering, vol. 30, no. 1, pp. 68-83, Jan. 2002 (doi: 10.1114/1.1433488).

[2] A. V. Hill, "The heat of shortening and the dynamic constant of muscle", Proceedings of The Royal Society B, vol. 126, no. 843, pp. 136-195, Oct. 1938 (https://doi.org/10.1098/rspb.1938.0050).

[3] Z. A. Hasan, "A model of spindle afferent response to muscle stretch", Journal of Neurophysiology, vol. 49, no. 4, pp. 989-1006, April 1983 (doi: 10.1152/jn.1983.49.4.989).   

[4] M. P. Mileusnic, J. E. Brown, N. Lan, G. E. Loeb, "Mathematical models of proprioceptors. I. control and transduction in the muscle spindle", Journal of Neurophysiology, vol. 96, pp. 1789-1802, Mar. 2006 (doi: 10.1152/jn.00868.2005).

[5] A. Prochazka, D. Gillard, D. J. Bennett, "Implications of positive feedback in the control of movement", Journal of Neurophysiology, vol. 77, Issue. 6, pp. 3237-3251, June. 1997 (doi: 10.1152/jn.1997.77.6.3237).

[6] A. S. Wexler, J. Ding, S. A. Binder-Macleod, "A mathematical model that predicts skeletal muscle force", IEEE Trans. on Biomedical Engineering, vol. 44, no. 5, pp. 337-348, May.1997.

[7] G. A. Mohammed, M. Hou, "Optimization of active muscle force–length models using least squares curve fitting", IEEE Trans. on Biomedical Engineering, vol. 63, no. 3, pp. 630-635, Mar. 2016 (doi: 10.1109/tbme. 2015.2467169).

[8] F. Toohidkhah, N. Lahimgarzadeh, Y. Mohammadali Morghi, "Motor control in humans", Amirkabir University Press, 1395 (in Persian).

 [9] A. M. Gordan, A. F. Huxley, F. J. Julian, "The variation in isometric tension with sarcomere length in vertebrate muscle fibers", Journal of Physiology, 184, pp. 170-192, 1966 (doi: 10.1113/jphysiol.1966. sp007909).

[10] U. Proske, S. C. Gandevia, "The proprioceptive senses: their roles in signaling body shape, body position and movement, and muscle force", Physiological Reviews, vol. 92, no. 4, pp. 1651-1697, Oct. 2012 (doi: 10.1152/physrev.00048.2011).

[11] S. Roatta, M. Passatore, "Muscle sensory receptors", Wiley, Encyclopedia of Biomedical Engineering, April 2006 (https://doi.org/10.1002/9780471740360.ebs0809).

[12] G. E. Loeb, M. Mileusnic, "Proprioceptors and models of transduction", Springer, Scholarpedia of Touch. Scholarpedia. Atlantis Press, Paris, pp. 437-465, Nov. 2016.

[13] U. Proske, S. C. Gandevia, "The proprioceptive senses: their roles in signaling body shape, body position and movement, and muscle force", Journal of Neurophysiolog, vol. 92, no. 4, pp. 1651-1697, Oct. 2012 (doi: 10.1152/physrev.00048.2011).

[14] M. P. Mileusnic, J. E. Brown, N. Lan, G. E. Loeb, "Mathematical models of proprioceptors. II. Structure and function of the golgi tendon organ", Journal of Neurophysiolgy, vol. 96, no. 4, pp. 1772-1788, Mar. 2006 (doi: 10.1152/jn.00869.2005).

[15] A. Zaknich, "Principles of adaptive filters and self-learning systems", Springer, Advanced Textbooks in Control and Signal processing Book Series, 2005.

[16] B. Widrow, J. McCool, M. Ball, "The complex LMS algorithm", Proceedings of IEEE, vol. 63, no. 4, April 1975 (doi: 10.1109/proc.1975.9807).

[17] I. Wiliams, T. G. Constandinou, "Computationally efficient modeling of proprioceptive signals in the upper limb for prostheses: a simulation study", Frontiers in Neuroscience, June. 2014 (doi: 10.3389/fnins. 2014.00181).

[18] J. E. Gregory, U. Proske, "The responses of golgi tendon organs to stimulation of different combinations of motor units", The Journal of Physiology, vol. 295, no. 1, pp. 251-262, Oct. 1979 (doi: 10.1113/jphysiol. 1979.sp012966).

[19] A. Prochazka, "Proprioceptive feedback and movement regulation", Comprehensive Physiology, Wiley, Jan. 2011 (doi: 10.1002/cphy. cp120103).

[20] W. Herzog, T. R. Leonard, "Force enhancement following stretching of skeletal muscle", Journal of Experimental Biology, pp. 1283-1275, 2002.